Question 535378: find all values of t in the interval [0,2pi] satisfying |sec(t)|= squareroot 2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find all values of t in the interval [0,2pi] satisfying |sec(t)|= squareroot 2
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sec t=√2
t=π/4
Normally, values of t would be found only in quadrants I and IV where sec>0
But with |sec t|=√2, you must also consider |-sec t|.
When you remove the absolute value bars the equation becomes -sec t=√2 or sec t=-√2, therefore, values of t would be found as well in quadrants II and III where sec<0, as follows:
t=π/4, 3π/4/ 5π/4 and 7π/4
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